On Hr(curl,Ω) estimates for a Maxwell type system in convex domains

In bounded convex domains, the regularity of a vector field u with its $\mathrm{div}\mathbf{u}$, $\mathrm{curl}\mathbf{u}$ in $L^r$ space and the tangential component or the normal component of u over the boundary in $L^r$ space, is established for $1<r<\infty$. As an application, we derive an $H^r(\mathrm{curl},\mathrm{\Omega })$ estimate for solutions to a Maxwell type system with an inhomogeneous boundary condition in convex domains. In contrast to the well-posed region of r in the space $H^r(\mathrm{curl},\mathrm{\Omega })$ for the Maxwell type system in Lipschitz domains given by Kar and Sini (2016) [16], we extend the well-posed region to be optimal.     

A Delayed HIV Infection Model with the Homeostatic Proliferation of CD4+ T Cells

Acta Mathematicae Applicatae Sinica, English Series - In this paper, we investigate a delayed HIV infection model that considers the homeostatic proliferation of CD4+ T cells. The existence and...     

Examples of compactλ-hypersurfaces in Euclidean spaces

In this paper,we first construct compact embeddedλ-hypersurfaces with the topology of torus which are calledλ-torus in Euclidean spaces?n^+1.Then,we give many compact immersedλ-hypersurfaces in Euclidean spaces?n^+1.     

On U(n)-invariant strongly convex complex Finsler metrics

Science China Mathematics - In this paper, we obtain a necessary and sufficient condition for a U(n)-invariant complex Finsler metric F on domains in ?n to be strongly convex, which also...     

Convergence of the viscosity solution of non-autonomous Hamilton-Jacobi equations

In this paper,we investigate the non-autonomous Hamilton-Jacobi equation ■ where H is 1-periodic with respect to t and M is a compact Riemannian manifold without boundary.We obtain the viscosity solution denoted by T_(t_0)~tφ(x) and show T_(t_0)~tφ(x) converges uniformly to a time-periodic viscosity solution u~*(x,t) of ?_tu+H(t,x,?_xu,u)=0.     

Activation energy process in hybrid CNTs and induced magnetic slip flow with heat source/sink

Effect of induced magnetic field is critical as a result of much controlled and focused on liquid flow is wanted in numerous modern and clinical procedures for example electromagnetic casting, drug delivery and cooling of nuclear reactors. Hence this investigation explains the behaviour of hybrid carbon nanotubes (CNTs) flow through slipped surface with induced magnetic field. Accumulation of SWCNTs (single wall) and MWCNTs (multi wall) nanomaterial with water base liquid is considered. Thermal performance is analyzed with regular heat source/sink effect. Chemical reaction and activation energy impacts are incorporated in mass equation. Solution of the similarity equations are obtained by adopting RKF45 method. Influence of flow variables are illustrated through graphs and computational values of drag force, Nusselt number and Sherwood number are presented in tables. It is noted that activation energy enhance the concentration field whereas opposite behaviour for reaction rate. Also induce magnetic field boosted with the larger values of magnetic Prandtl number. Furthermore it is observed that hybrid CNTs nanomaterial having higher rate of heating/cooling compare to singular CNTs nanomaterial.     

Stability analysis of fractional order fuzzy cellular neural networks with leakage delay and time varying delays

In this paper we investigated the stability of fractional order fuzzy cellular neural networks with leakage delay and time varying delays. Based on Lyapunov theory and applying bounded techniques of fractional calculation, sufficient criterion are established to guarantee the stability. Hybrid feedback control is applied to derive the proposed results. Finally, numerical examples with simulation results are given to illustrate the effectiveness of the proposed method.